Subgroups — #88543

Order 432.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	#6226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#3754	—	3	1	no	maximal
5	#3672	—	3	3	no	maximal
6	C₂²×C₃×C₉	—	2	1	no	—
7	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₃⋊Dic₉	—	2	1	no	—
9	C₃²×D₄	D₃	1	1	yes	characteristic
10	#634	—	3	1	no	—
11	C₃⋊(C₃⋊C₈)	—	3	1	no	—
12	D₄×C₉	D₃	1	3	yes	—
13	Dic₁₈	—	3	3	no	—
14	C₉⋊C₈	—	3	3	no	—
15	C₂×C₃×C₉	—	4	1	no	—
16	C₂×C₃×C₉	D₄	1	1	yes	characteristic
17	#214	—	9	3	no	—
18	#214	—	9	1	no	—
19	C₂²×C₃²	—	2	1	no	—
20	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
21	C₃⋊Dic₃	—	6	1	no	—
22	C₂²×C₉	—	2	3	no	—
23	C₄×C₉	C₂×D₃	1	3	yes	—
24	Dic₉	—	6	3	no	—
25	C₃×C₉	SD₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₃×D₄	D₉	1	3	yes	—
27	C₃×D₄	C₃⋊D₃	1	1	yes	characteristic
28	Dic₆	—	9	3	no	—
29	Dic₆	—	9	1	no	—
30	C₃⋊C₈	—	9	3	no	—
31	C₃⋊C₈	—	9	1	no	—
32	C₂×C₃²	—	4	1	no	—
33	C₂×C₃²	#67	1	1	yes	characteristic
34	C₂×C₉	—	4	3	no	—
35	C₂×C₉	#67	1	3	yes	—
36	SD₁₆	—	27	1	no	Sylow
37	C₂²×C₃	—	2	3	no	—
38	C₂²×C₃	—	2	1	no	—
39	C₃×C₄	C₂×D₉	1	3	yes	—
40	C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
41	Dic₃	—	18	3	no	—
42	Dic₃	—	18	1	no	—
43	C₃²	#214	1	1	yes	characteristic
44	C₉	#214	1	3	yes	complemented
45	Q₈	—	27	1	no	—
46	D₄	C₃⋊D₉	1	1	yes	characteristic
47	C₈	—	27	1	no	—
48	C₂×C₃	—	4	3	no	—
49	C₂×C₃	—	4	1	no	—
50	C₂×C₃	#611	1	3	yes	—
51	C₂×C₃	#638	1	1	yes	characteristic
52	C₂²	—	2	1	no	—
53	C₄	—	54	1	no	—
54	C₄	C₂×C₃⋊D₉	1	1	yes	characteristic
55	C₃	#3672	1	3	yes	complemented
56	C₃	#3754	1	1	yes	characteristic
57	C₂	—	4	1	no	—
58	C₂	#6233	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#6233
commutator, cosocle	C₃×C₄×C₉	C₂²
Frattini	C₃×C₄	C₂×C₃⋊D₃
Fitting	C₃×D₄×C₉	C₂
socle	C₂×C₃²	#67
prime radical	C₃²×D₄	D₃
hypercenter	D₄	C₃⋊D₉
hypocenter	C₃×C₉	SD₁₆
LCS	G ▷ C₃×C₄×C₉ ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #6226	C₂	semidirect
3. C₃⋊(C₉⋊C₈)	C₂	semidirect
25. C₃×C₉	SD₁₆	semidirect
44. C₉	#214	semidirect
55. C₃	#3672	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₄×C₉	2
#6226	2
C₃⋊(C₉⋊C₈)	2
#3754	3
#3672	3